How can I force input to be interpreted as millimetres instead of metres?
You can do that from the Scene panel, Under Units, Scale 1.0000000 means that it's in meters, change it to 0.01, this will make your units in cm, or 0.001 will make them in mm.
Be careful though if you're planning to export your objects to a different software, like UE4 for instance, you need to change this later to meet the requirements of that software.


Edit:Make sure that you also change the scale in 3D View window, under Display (in the properties shelve to your right hand by default, if you can't see that, press N while hovering over 3D View window).
Check this answer too: Change the scale of the viewport